Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method in 2D and 3D that addresses this challenge and efficiently handles meshes with intricate structures. Additionally, we present an algorithm that adapts the mesh resolution to local geometry in 2D for efficient representation. We demonstrate the effectiveness of our approach on 2D point cloud and 3D multi-view reconstruction tasks. Visit our project page (https://sonsang.github.io/dmesh2-project) for source code and supplementary material.

Various heuristic objectives for modeling hand-object interaction have been proposed in past work. However, due to the lack of a cohesive framework, these objectives often possess a narrow scope of applicability and are limited by their efficiency or accuracy. In this paper, we propose HANDYPRIORS, a unified and general pipeline for pose estimation in human-object interaction scenes by leveraging recent advances in differentiable physics and rendering. Our approach employs rendering priors to align with input images and segmentation masks along with physics priors to mitigate penetration and relative-sliding across frames. Furthermore, we present two alternatives for hand and object pose estimation. The optimization-based pose estimation achieves higher accuracy, while the filtering-based tracking, which utilizes the differentiable priors as dynamics and observation models, executes faster. We demonstrate that HANDYPRIORS attains comparable or superior results in the pose estimation task, and that the differentiable physics module can predict contact information for pose refinement. We also show that our approach generalizes to perception tasks, including robotic hand manipulation and human-object pose estimation in the wild.

As industrial models and designs grow increasingly complex, the demand for optimal control of large-scale dynamical systems has significantly increased. However, traditional methods for optimal control incur significant overhead as problem dimensions grow. In this paper, we introduce an end-to-end quantum algorithm for linear-quadratic control with provable speedups. Our algorithm, based on a policy gradient method, incorporates a novel quantum subroutine for solving the matrix Lyapunov equation. Specifically, we build a *quantum-assisted differentiable simulator* for efficient gradient estimation that is more accurate and robust than classical methods relying on stochastic approximation. Compared to the classical approaches, our method achieves a *super-quadratic* speedup. To the best of our knowledge, this is the first end-to-end quantum application to linear control problems with provable quantum advantage.

Embedding polygonal mesh assets within photorealistic Neural Radience Fields (NeRF) volumes, such that they can be rendered and their dynamics simulated in a physically consistent manner with the NeRF, is under-explored from the system perspective of integrating NeRF into the traditional graphics pipeline. This paper designs a two-way coupling between mesh and NeRF during rendering and simulation. We first review the light transport equations for both mesh and NeRF, then distill them into an efficient algorithm for updating radiance and throughput along a cast ray with an arbitrary number of bounces. To resolve the discrepancy between the linear color space that the path tracer assumes and the sRGB color space that standard NeRF uses, we train NeRF with High Dynamic Range (HDR) images. We also present a strategy to estimate light sources and cast shadows on the NeRF. Finally, we consider how the hybrid surface-volumetric formulation can be efficiently integrated with a high-performance physics simulator that supports cloth, rigid and soft bodies. The full rendering and simulation system can be run on a GPU at interactive rates. We show that a hybrid system approach outperforms alternatives in visual realism for mesh insertion, because it allows realistic light transport from volumetric NeRF media onto surfaces, which affects the appearance of reflective/refractive surfaces and illumination of diffuse surfaces informed by the dynamic scene.

We introduce a novel policy learning method that integrates analytical gradients from differentiable environments with the Proximal Policy Optimization (PPO) algorithm. To incorporate analytical gradients into the PPO framework, we introduce the concept of an α-policy that stands as a locally superior policy. By adaptively modifying the α value, we can effectively manage the influence of analytical policy gradients during learning. To this end, we suggest metrics for assessing the variance and bias of analytical gradients, reducing dependence on these gradients when high variance or bias is detected. Our proposed approach outperforms baseline algorithms in various scenarios, such as function optimization, physics simulations, and traffic control environments. Our code can be found online: https://github.com/SonSang/gippo.

Reflectional symmetry is a ubiquitous pattern in nature. Previous works usually solve this problem by voting or sampling, suffering from high computational cost and randomness. In this article, we propose a learning-based approach to intrinsic reflectional symmetry detection. Instead of directly finding symmetric point pairs, we parametrize this self-isometry using a functional map matrix, which can be easily computed given the signs of Laplacian eigenfunctions under the symmetric mapping. Therefore, we manually label the eigenfunction signs for a variety of shapes and train a novel neural network to predict the sign of each eigenfunction under symmetry. Our network aims at learning the global property of functions and consequently converts the problem defined on the manifold to the functional domain. By disentangling the prediction of the matrix into separated bases, our method generalizes well to new shapes and is invariant under perturbation of eigenfunctions. Through extensive experiments, we demonstrate the robustness of our method in challenging cases, including different topology and incomplete shapes with holes. By avoiding random sampling, our learning-based algorithm is over 20 times faster than state-of-the-art methods, and meanwhile, is more robust, achieving higher correspondence accuracy in commonly used metrics.

We formulate the first differentiable analog quantum computing framework with specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by {\em orders of magnitude}.

We present a method for learning 3D geometry and physics parameters of a dynamic scene from only a monocular RGB video input. To decouple the learning of underlying scene geometry from dynamic motion, we represent the scene as a time-invariant signed distance function (SDF) which serves as a reference frame, along with a time-conditioned deformation field. We further bridge this neural geometry representation with a differentiable physics simulator by designing a two-way conversion between the neural field and its corresponding hexahedral mesh, enabling us to estimate physics parameters from the source video by minimizing a cycle consistency loss. Our method also allows a user to interactively edit 3D objects from the source video by modifying the recovered hexahedral mesh, and propagating the operation back to the neural field representation. Experiments show that our method achieves superior mesh and video reconstruction of dynamic scenes compared to competing Neural Field approaches, and we provide extensive examples which demonstrate its ability to extract useful 3D representations from videos captured with consumer-grade cameras.

We introduce a novel differentiable hybrid traffic simulator , which simulates traffic using a hybrid model of both macroscopic and microscopic models and can be directly integrated into a neural network for traffic control and flow optimization. This is the first differentiable traffic simulator for macroscopic and hybrid models that can compute gradients for traffic states across time steps and inhomogeneous lanes. To compute the gradient flow between two types of traffic models in a hybrid framework, we present a novel intermediate conversion component that bridges the lanes in a differentiable manner as well. We also show that we can use analytical gradients to accelerate the overall process and enhance scalability. Thanks to these gradients, our simulator can provide more efficient and scalable solutions for complex learning and control problems posed in traffic engineering than other existing algorithms. Refer to https://sites.google.com/umd.edu/diff-hybrid-traffic-sim for our project.

3D models are commonly used in computer vision and graphics. With the wider availability of mesh data, an efficient and intrinsic deep learning approach to processing 3D meshes is in great need. Unlike images, 3D meshes have irregular connectivity, requiring careful design to capture relations in the data. To utilize the topology information while staying robust under different triangulations, we propose to encode mesh connectivity using Laplacian spectral analysis, along with mesh feature aggregation blocks (MFABs) that can split the surface domain into local pooling patches and aggregate global information amongst them. We build a mesh hierarchy from fine to coarse using Laplacian spectral clustering, which is flexible under isometric transformations. Inside the MFABs there are pooling layers to collect local information and multi-layer perceptrons to compute vertex features of increasing complexity. To obtain the relationships among different clusters, we introduce a Correlation Net to compute a correlation matrix, which can aggregate the features globally by matrix multiplication with cluster features. Our network architecture is flexible enough to be used on meshes with different numbers of vertices. We conduct several experiments including shape segmentation and classification, and our method outperforms state-of-the-art algorithms for these tasks on the ShapeNet and COSEG datasets.

Synthesizing realistic 3D mesh deformation sequences is a challenging but important task in computer animation. To achieve this, researchers have long been focusing on shape analysis to develop new interpolation and extrapolation techniques. However, such techniques have limited learning capabilities and therefore often produce unrealistic deformation. Although there are already networks defined on individual meshes, deep architectures that operate directly on mesh sequences with temporal information remain unexplored due to the following major barriers: irregular mesh connectivity, rich temporal information, and varied deformation. To address these issues, we utilize convolutional neural networks defined on triangular meshes along with a shape deformation representation to extract useful features, followed by long short-term memory (LSTM) that iteratively processes the features. To fully respect the bidirectional nature of actions, we propose a new share-weight bidirectional scheme to better synthesize deformations. An extensive evaluation shows that our approach outperforms existing methods in sequence generation, both qualitatively and quantitatively.

We introduce an efficient differentiable fluid simulator that can be integrated with deep neural networks as a part of layers for learning dynamics and solving control problems. It offers the capability to handle one-way coupling of fluids with rigid objects using a variational principle that naturally enforces necessary boundary conditions at the fluid-solid interface with sub-grid details. This simulator utilizes the adjoint method to efficiently compute the gradient for multiple time steps of fluid simulation with user defined objective functions. We demonstrate the effectiveness of our method for solving inverse and control problems on fluids with one-way coupled solids. Our method outperforms the previous gradient computations, state-of-the-art derivative-free optimization, and model-free reinforcement learning techniques by at least one order of magnitude.

We present a method for efficient differentiable simulation of articulated bodies. This enables integration of articulated body dynamics into deep learning frameworks, and gradient-based optimization of neural networks that operate on articulated bodies. We derive the gradients of the contact solver using spatial algebra and the adjoint method. Our approach is an order of magnitude faster than autodiff tools. By only saving the initial states throughout the simulation process, our method reduces memory requirements by two orders of magnitude. We demonstrate the utility of efficient differentiable dynamics for articulated bodies in a variety of applications. We show that reinforcement learning with articulated systems can be accelerated using gradients provided by our method. In applications to control and inverse problems, gradient-based optimization enabled by our work accelerates convergence by more than an order of magnitude.

We present a method for differentiable simulation of soft articulated bodies. Our work enables the integration of differentiable physical dynamics into gradient-based pipelines. We develop a top-down matrix assembly algorithm within Projective Dynamics and derive a generalized dry friction model for soft continuum using a new matrix splitting strategy. We derive a differentiable control framework for soft articulated bodies driven by muscles, joint torques, or pneumatic tubes. The experiments demonstrate that our designs make soft body simulation more stable and realistic compared to other frameworks. Our method accelerates the solution of system identification problems by more than an order of magnitude, and enables efficient gradient-based learning of motion control with soft robots.

Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We develop a scalable framework for differentiable physics that can support a large number of objects and their interactions. To accommodate objects with arbitrary geometry and topology, we adopt meshes as our representation and leverage the sparsity of contacts for scalable differentiable collision handling. Collisions are resolved in localized regions to minimize the number of optimization variables even when the number of simulated objects is high. We further accelerate implicit differentiation of optimization with nonlinear constraints. Experiments demonstrate that the presented framework requires up to two orders of magnitude less memory and computation in comparison to recent particle-based methods. We further validate the approach on inverse problems and control scenarios, where it outperforms derivative-free and model-free baselines by at least an order of magnitude.

Transferring deformation from a source shape to a target shape is a very useful technique in computer graphics. State-of-the-art deformation transfer methods require either point-wise correspondences between source and target shapes, or pairs of deformed source and target shapes with corresponding deformations. However, in most cases, such correspondences are not available and cannot be reliably established using an automatic algorithm. Therefore, substantial user effort is needed to label the correspondences or to obtain and specify such shape sets. In this work, we propose a novel approach to automatic deformation transfer between two unpaired shape sets without correspondences. 3D deformation is represented in a high-dimensional space. To obtain a more compact and effective representation, two convolutional variational autoencoders are learned to encode source and target shapes to their latent spaces. We exploit a Generative Adversarial Network (GAN) to map deformed source shapes to deformed target shapes, both in the latent spaces, which ensures the obtained shapes from the mapping are indistinguishable from the target shapes. This is still an under-constrained problem, so we further utilize a reverse mapping from target shapes to source shapes and incorporate cycle consistency loss, i.e. applying both mappings should reverse to the input shape. This VAE-Cycle GAN (VC-GAN) architecture is used to build a reliable mapping between shape spaces. Finally, a similarity constraint is employed to ensure the mapping is consistent with visual similarity, achieved by learning a similarity neural network that takes the embedding vectors from the source and target latent spaces and predicts the light field distance between the corresponding shapes. Experimental results show that our fully automatic method is able to obtain high-quality deformation transfer results with unpaired data sets, comparable or better than existing methods where strict correspondences are required.